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If |x+1/2|=|y+1/2|, what is the value of x+y?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 800 Q59 V59
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If |x+1/2|=|y+1/2|, what is the value of x+y? [#permalink]

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New post 20 Mar 2018, 01:45
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[GMAT math practice question]

If \(|x+\frac{1}{2}|=|y+\frac{1}{2}|\), what is the value of \(x+y\)?

1) \(xy<0\)
2) \(x>0\) and \(y<0\)
[Reveal] Spoiler: OA

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Re: If |x+1/2|=|y+1/2|, what is the value of x+y? [#permalink]

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New post 20 Mar 2018, 02:55
MathRevolution wrote:
[GMAT math practice question]

If \(|x+\frac{1}{2}|=|y+\frac{1}{2}|\), what is the value of \(x+y\)?

1) \(xy<0\)
2) \(x>0\) and \(y<0\)


\(|x+\frac{1}{2}|=|y+\frac{1}{2}|\)

Two cases possible..
1) x and y are of SAME sign
x=y..
Then x and y can take any value.. and thus x+y could be anything..

2) x and y are of different sign...
x+1/2 = -y-1/2......x+y=-1

So we can get a value of x+y if they both are of OPPOSITE sign..

Let's see what each statement tells us..
(I) xy<0
X and y are of OPPOSITE sign..
Hence x+y=-1
Sufficient
(II) x>0 and y<0..
So both are OPPOSITE sign..
Suff

D
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5255
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: If |x+1/2|=|y+1/2|, what is the value of x+y? [#permalink]

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New post 22 Mar 2018, 00:50
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

\(|x+\frac{1}{2}|=|y+\frac{1}{2}|\)
\(=> |x+\frac{1}{2}|^2=|y+\frac{1}{2}|^2\)
\(=> (x+\frac{1}{2})^2=(y+\frac{1}{2})^2\)
\(=> x^2 + x + \frac{1}{4} = y^2 + y + \frac{1}{4}\)
\(=> x^2 - y^2 + x - y = 0\)
\(=> (x-y)(x+y)+(x-y) = 0\)
\(=> (x-y)(x+y+1) = 0\)
\(=> x=y or x+y=-1\)

Condition 1)
Since \(xy < 0\), we have \(x≠y\) and \(x+y = -1\) from the original condition.

Condition 2)
Since \(x > 0\) and \(y < 0\), we have \(x≠y\) and\(x+y = -1\)from the original condition.

Therefore, D is the answer.

By Tip 1), D is most likely to be the answer.

Answer: D
_________________

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: If |x+1/2|=|y+1/2|, what is the value of x+y?   [#permalink] 22 Mar 2018, 00:50
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